Coexistence of partially disordered/ordered phases in an extended Potts model

We consider a generalization of the standard Potts model in which then are q=r+s states with an interaction that distinguishes the two subspecies. We develop a graphical representation (of the FK type) for the system and show that this representation may be incorporated directly into reflection posi tivity arguments. Using combinations of these techniques, we establish deta iled properties of the phase diagram including the existence of sharp tripl e points. Whenever relevant, the phases are characterized by the percolatio n properties of the underlying representation.